How do I solve this? Please refrain from using other solutions.
4. A particle with mass m and energy E is incident from the left on the potential energy diagram shown in the picture on the right. The barrier has an energy Uo>E.The region to the right of the barrier has an energy Uo below region 1.
iUo
iUo
0
L
a. Write down the boundary conditions for Schrodinger's equation in regions 1, 2 and 3. (2 pts.)
b. Write down the functional form of the wavefunctions in all three regions including any terms in the function (e.g., sinh(kx) where k = VU.. ) (3 pts.)
c. Write down the wavelength of the wavefunctions in the regions where they are oscillatory. Do they have the same value ? (2 pts.)
The transmission coefficient (e.g., T = 1411 1 1 U2 T 1+ke-2x where k = 4Uo-E
e. Write an approximate expression for the ratio of T if the barrier height is doubled
f. How much does the probability of tunneling change if the Transmission coefficient (T) is doubled? (1 pt.)